The Young European Queueing Theorists (YEQT) workshops are
organized on a yearly basis at Eurandom, Eindhoven.
The aim of these workshops is to bring together young researchers (PhD students,
postdocs, or recently appointed lecturers or assistant professors) to share and
discuss research related to queueing theory.
In addition, a few leading researchers give a tutorial or keynote lecture, so as
to inspire the young researchers.
YEQT-VII will be the seventh edition of the Young European Queueing Theorists
workshop, and will take place in November 4-6, 2013, at Eurandom.
The event provides an excellent opportunity for developing researchers to
interact and present their research findings.
YEQT provides a friendly, yet research focused, venue for this purpose.

Keynote speakers will be Rhonda Righter (Berkeley University), Rami Atar
(Technion) and Joris Walraevens (Ghent University).
The tutorials will be given by Michael Harrison (Stanford University) and
Richard Weber (University of Cambridge).

During the workshop there will be time and space available to
present scientific posters. We especially invite young researchers to come
forward with a poster on their recent work. Please email
Patty Koorn with your request
and we will do our best to accommodate your poster.

Approximations for the waiting time distribution in
an M/G/c priority queue

We investigate the use of priority mechanisms when assigning service
engineers to customers as a tool for service differentiation. To this end,
we analyze a non-preemptive 𝑀/𝐺/𝑐 priority queue with various customer
classes. For this queue, we present various accurate and fast methods to
estimate the first two moments of the waiting time per class given that all
servers are occupied. These waiting time moments allow us to characterize
the overall waiting time distribution per class. We subsequently apply these
methods to real-life data in a case study.

There is a vast literature on heavy traffic analysis of controlled
queueing models at the diffusion scale. In this talk I will describe recent
developments on the alternative approach that considers these models at the
moderate deviation scale.

Retrial queueing systems are
characterized by the feature that an arriving customer who finds all the
servers busy leaves the system and repeats his demand after a random amount
of time. In such a case we assume that the blocked customer joins a virtual
queue, called the orbit queue. In this work we study a single server retrial
queueing system accepting n types of customers. We assume that customers of
type i have preemptive priority over customers of type j, i <
j. Customers of type 1 are queued in an infinite capacity ordinary
queue and served in a FIFO discipline. An arriving type 1 customer who finds
the server busy with a customer of type i (i = 2, ..., n)
pushes him in his own orbit and occupy the server. The behavior of customers
of type i, i = 2, ..., n is described as follows. If a newly
arriving customer of type i, i = 2, ..., n finds the server
busy with a customer of type j, where i < j, pushes the
customer in service in his own orbit and occupy the server. Otherwise the
newly arriving customer of type i, is blocked and routed to a
seperate type i orbit queue. Both blocked and interrupted customers
of type i, i = 2, ..., n, leave the system and repeat their
demand individually after an exponentially distributed amount of time. Such
a queueing system serves as a model for competing job streams in a carrier
sensing multiple access system. We study the queueing system using
multi-dimensional probability generating functions. For such a model we
obtain the mean number of type i (i = 1, 2, ..., n)
customers in steady state and use them to draw conclusions from numerical
calculations.

We discuss the problem of
scheduling stochastic jobs in a single-server system, where the capacity of
the system varies over time. The Gittins' index policy, which is known to be
optimal in systems with constant capacity, turns out to be suboptimal in the
general case. However, Glazebrook 87 showed the optimality of Gittins' index
in ON-OFF systems with geometric ON periods. We give an alternative proof
for this result, provide a new expression for the index, and use it to
characterize the optimal policy when the service time distributions have
some specific properties.

Traditionally, research focusing on
the design of scheduling and staffing policies for service systems has
modeled servers as having fixed (possibly heterogeneous) service rates.
However, service systems are often staffed by people. Then, the rate a
server chooses to work may be impacted by the scheduling and staffing
policies used by the system. We present a model for such "strategic
servers'' that choose their service rate in order to maximize a trade-off
between an "effort cost'', which captures the idea that servers exert more
effort when working at a faster rate, and a "value of idleness'', which
assumes that servers prefer to be idle as much as possible. We re-visit
routing and staffing questions for an M/M/N system in this strategic server
framework. First, we establish the conditions for the existence of a
symmetric equilibrium service rate under any idle-time-order-based routing
policy. Then, we find the staffing level that asymptotically minimizes
linear staffing and waiting costs as the arrival rate grows large. An
important interesting insight is that that asymptotically optimal staffing
level staffs many more servers (of the order of the arrival rate more) than
the common square-root staffing policy that has been shown to be
asymptotically optimal in the conventional M/M/N setting, when servers are
not strategic.

A multi-class M/M/1 system, with service rate $\mu_in$ for class-$i$
customers, is considered with the risk-sensitive cost criterion $n^{-1}\log
E\exp\sum_ic_iX^n_i(T)$, where $c_i>0$, $T>0$ are constants, and $X^n_i(t)$
denotes the class-$i$ queue-length at time $t$, assuming the system starts
empty. An asymptotic upper bound (as $n->\infinity$) on the performance
under a fixed priority policy is attained, implying that the policy is
asymptotically optimal when $c_i$ are sufficiently large. The analysis is
based on the study of an underlying differential game.
(joint work with Rami Atar and Adam Shwartz)

This tutorial will focus on single-hop stochastic processing networks.
That is, in the network models to be considered, arriving jobs of various
types each require a single service before departing, but that service may
be obtainable from several different servers, or may require capacity
allocations from several servers simultaneously. In the heavy traffic
parameter regime, the dynamic scheduling problem for the processing network
is formally approximated by a corresponding Brownian control problem (BCP).
In all cases the approximating BCP is more tractable than the conventional
scheduling problem that it replaces. In particular, the approximating BCP
may have a smaller effective dimension than the original problem, and if its
effective dimension is one, then the approximating BCP can be solved
explicitly. Many open problems remain, especially concerning the translation
of Brownian solutions back into the conventional model context.

We
investigate how to share a common resource among multiple classes of
customers in the presence of abandonments. We consider two different models:
(1) customers can abandon both while waiting in the queue and while being
served, (2) only customers that are in the queue can abandon. Given the
complexity of the stochastic optimization problem we propose a fluid model
as a deterministic approximation. For the overload case we directly obtain
that the $\tilde c \mu$-rule is optimal. For the underload case we use
Pontryagin's Maximum Principle to obtain the optimal solution for two
classes of customers; there exists a switching curve that splits the
two-dimensional state-space into two regions such that when the number of
customers in both classes is sufficiently small the optimal policy follows
the $\tilde c \mu$-rule and when the number of customers is sufficiently
large the optimal policy follows the $\tilde c μ-rule.
The same structure is observed numerically in the optimal policy of the
stochastic model for an arbitrary number of classes. Based on this we
develop a heuristic and by numerical experiments we evaluate its performance
and compare it to several index policies. We observe that the suboptimality
gap of our solution is small.

We consider a single-hop switched
queueing network with a mix of heavy-tailed (i.e., arrival processes with
infinite variance) and light-tailed traffic, and study the delay performance
of the Max-Weight policy, known for its throughput optimality and asymptotic
delay optimality properties.
Classical results in queueing theory imply that heavy-tailed queues are
delay unstable, i.e., they experience infinite expected delays in steady
state. Thus, we focus on the impact of heavy-tailed traffic on the
light-tailed queues, using delay stability as performance metric. Recent
work has shown that this impact may come in the form of subtle
rate-dependent phenomena, the
stochastic analysis of which is quite cumbersome. Our goal is to show how
fluid approximations can facilitate the delay analysis of the Max-Weight
policy under heavy-tailed traffic. More specifically, we show how fluid
approximations can be combined with renewal theory in order to prove delay
instability results. Furthermore, we show how fluid approximations can be
combined with stochastic Lyapunov theory in order to prove delay stability
results. We illustrate the benefits
of the proposed approach in two ways: (i) analytically, by providing a sharp
characterization of the delay stability regions of networks with disjoint
schedules, significantly generalizing previous results; (ii)
computationally, through a Bottleneck Identification algorithm, which
identifies (some) delay unstable queues by solving the fluid model of the
network from certain initial conditions.

We consider the intercell coordination problem
between two interfering cells combined with dynamic TDD. In dynamic TDD,
each station selects whether it is serving uplink (u) or downlink (d)
traffic. Thus, the system has four possible operation modes (uu, du, ud, dd).
The amount of intercell interference between the stations clearly depends on
the operation mode. Traffic in our model consists of elastic data flows in
both cells (cells 1 and 2) and in both directions (uplink and downlink),
i.e., there are four traffic classes. Flows in each class are served
according to the processor sharing (PS) queueing discipline. We first
characterize the maximal stability region, and then determine the optimal
static (i.e., state-independent) policy to choose the operation mode for
various scenarios. We also consider further optimizing the performance by
dynamic policies, where the chosen operation mode depends on the
instantaneous state of the system. We define several dynamic priority
policies and also consider the policy resulting from applying the first
policy iteration algorithm to the optimal static policy. In addition, as a
reference policy, we have the well-known max-weight policy. We show that
certain simple priority policies are, in fact, stochastically optimal in
some special cases, but which policy is optimal depends on the setting. In
the general case, we simulate the performance of the dynamic policies and
give insight into how the policies perform relative to each other and what
is the ultimate gain achieved by the dynamic policies.

A first order performance characterization of queueing systems is the
stability region. We study the relation of system stability to minimal
evacuation times, i.e. the necessary time to clear specific snapshots of
packets. It is shown that under certain conditions the stability region is
completely characterized by the asymptotic growth of the evacuation
function. This in turn can be determined in closed form for specific
systems, which makes the proposed tool very useful.
We focus on the example of input queued switches to illustrate the interplay
between the original system with arrivals and the model with snapshot
evacuation. Although optimal evacuation policies are always throughput
optimal (even the asymptotically optimal ones), well known throughput
optimal policies such as maxweight scheduling are shown to be asymptotically
suboptimal with respect to evacuation times. Furthermore, we show that given
any throughput optimal policy, a randomized version of it that is
asymptotically optimal can be designed.
Then we examine applications of the proposed tool. In particular we consider
wireless network coding, index coding, broadcast erasure channel and
opportunistic routing and showcase how this tool can be used.

Customers are often faced with a
choice of when to arrive to a congested queue with some desired service at
the end. Suppose the server operates for a certain time interval, and
customers are served according to their arrival order. Typically, customers
wish to avoid waiting in the queue for a long time, but arriving too late or
too early may also incur high costs. We model the interaction between the
customers arriving to the queue as a strategic game. Examples of such
scenarios are arriving at a concert with unmarked seats, driving to work in
the morning or going to lunch in the cafeteria. We will examine an example
in which customers incur costs according to their order of arrival.
Specifically, an arrival process that constitutes a Nash Equilibrium will be
presented.

Determining the structure, properties, and
particular values of optimal policies for minimizing a global (social)
objective function for scheduling and routing problems is often extremely
difficult using standard approaches such as dynamic programming. On the
other hand, given a priority order, individually optimal (selfish)
scheduling policies are often structurally obvious and easily computed. We
show how to make the social and selfish solutions coincide by assigning
appropriate priorities to individuals, and apply the approach to optimal
"green" scheduling (with both holding costs and energy usage costs) and to
marginal analysis of flexibility in service systems such as call centers.
(joint work with Osman Akgun (Bailard), Doug Down (McMasterUniversity) and
Ron Wolff (UC Berkeley)

We develop
many-server asymptotics in the Quality-and-Efficiency-Driven (QED) regime
for models with admission control. The admission control, designed to reduce
the incoming traffic in periods of congestion, scales with the size of the
system. For a class of Markovian models with this scaled control, we
identify the QED limits for two stationary performance measures. We also
derive corrected QED approximations, generalizing earlier results for the
Erlang B, C and A models. These results are useful for the dimensioning of
large systems equipped with an active control policy. In particular, the
corrected approximations can be leveraged to establish the optimality gaps
related to square-root staffing and asymptotic dimensioning with admission
control.

A functional
central limit theorem for a Markov-modulated infinite-server queue

We model the
production of new molecules in a chemical reaction network as a Poisson
process with a varying arrival rate, depending on an external Markov
process. It is assumed that the molecules decay after an exponential time,
independently of other molecules present. The goal is to analyze the
distributional properties of the number of molecules in the system, under a
specific time-scaling. In this scaling, the background process is sped up by
a factor N^\alpha, for some \alpha>0, whereas the arrival rates are scaled
by N, for N large.
By applying the martingale central limit theorem, we show that the number of
molecules, after centering and scaling, converges weakly to an Ornstein-Uhlenbeck
process, thus obtaining a functional central limit theorem (F-CLT). An
interesting dichotomy is observed, namely, if \alpha>1 the background
process jumps faster than the arrival process, and consequently the arrival
process behaves essentially as a (homogeneous) Poisson process, so that the
scaling in the F-CLT is the usual \sqrt{N}, whereas for \alpha <= 1 the
background process is relatively slow, and the scaling in the F-CLT is
N^{1-\alpha/2}. In the latter regime, the parameters of the limiting
Ornstein-Uhlenbeck process contain the deviation matrix associated with the
background process.

With ever-increasing demands for bandwidth optical
packet/burst switching is used to utilise more of the available capacity of
optical networks. In current prototypes of optical switches time and
wavelength multiplexing are combined to resolve packet contentions, by means
of Fiber Delay Lines and wavelength converters in the switching elements.
Although optical switches have lower energy consumption than their
electronic counterparts, it remains substantial. Since wavelength converters
contribute significantly to the switches overall energy consumption, they
should be used sparingly, rather than continuously. Current scheduling
algorithms however do not take the usage of wavelength converters (and the
related effectiveness) into account. To this end, we developed and evaluated
new cost-based scheduling algorithms, which take both gap and delay into
account to schedule an incoming packet. The performance improvement of these
algorithms over existing algorithms can be traded off for a significant
reduction in up-time of the wavelength converters by introducing a
conversion cost in the involved cost function. This is backed by Monte Carlo
simulation results, in which the algorithms are applied both in a
void-filling and non-void-filling setting. The algorithms are of the same
implementation complexity as current algorithms, and thus of immediate value
to switch designers.(joint work with Wouter Rogiest, Herwig Bruneel)

Tail probabilities of the number of customers and
the customer delay of the low-priority class in a two-class infinite
priority queue are investigated. The tool used is singularity analysis of
probability generating functions, by which it is shown that different (types
of) singularities of the respective probability generating function might
play a role, leading to distinct asymptotics. We categorize the possible
asymptotics either as (i) exponential, (ii) power law or (iii) power law
with exponential cut-off. The analytic work is complemented by stochastic
intuition, in that the different types of asymptotics are the result of the
dominance of different effects in the queue, namely, resp. a queueing
effect, a single-event effect and a priority effect. We also look at what
happens when the queue is near the instability bound, and at the influence
of finite high-priority buffer capacity.
(joint work with T. Demoor, T. Maertens, D. Fiems and H. Bruneel)

We consider the problem of optimal control for a
number of alternative Markov decision processes, where at each moment in
time exactly one process must be "continued" while all other processes are
"frozen". Only the process that is continued produces any reward and changes
its state. The aim is to maximize expected total discounted reward. A
familiar example would be the problem of optimally scheduling the processing
of jobs that reside in a single-server queue. A each moment one of the jobs
is processed by the server, while all the other jobs are made to wait. Our
aim is to minimize the expected total holding cost incurred until all jobs
are complete. Another example is that of hunting for an apartment; we must
choose the order in which to view apartments and decide when to stop viewing
and rent the best apartment of those that have been viewed. This type of
problem has a beautiful and surprising solution in terms of Gittins indices.
In this tutorial I will review the theory of bandit processes and Gittins
indices, describe some applications in scheduling and queueing, and tell you
about some frontiers of research in the field.

In this talk I will first discuss some general ideas
on modeling and optimization of data backup scheduling, an increasingly
important problem domain in which no formal mathematical model has been
proposed before. Then I will present some queueing-type results on
distributed data backup scheduling that we obtained motivated by a
real-world project at IBM. Specifically, we developed a novel Markov chain
model to describe the distributed data backup process and analyzed its
stability conditions and stationary behavior. In the context of our proposed
model, we also formulated an optimization problem for choosing a scheduling
policy that strikes the right balance between performing frequent backups to
improve data safety and reducing backup costs.

●Travel

For those arriving by plane, there is a convenient direct
train connection between Amsterdam Schiphol airport and Eindhoven. This trip
will take about one and a half hour. For more detailed information, please
consult the NS travel information
pages or see Eurandom web page location.

Many low cost carriers also fly to Eindhoven Airport.
There is a bus connection to the Eindhoven central railway station from the
airport. (Bus route number 401) For details on departure times consult http://www.9292ov.nl

●Conference facilities : Conference
room, Metaforum Building MF11&12

The meeting-room is equipped with a data projector, an
overhead projector, a projection screen and a blackboard. Please note that
speakers and participants making an oral presentation are kindly requested to
bring their own laptop or their presentation on a memory stick.

●Conference Secretariat

Upon arrival, participants should register with the
workshop officer, and collect their name badges. The workshop officer will be
present for the duration of the conference, taking care of the administrative
aspects and the day-to-day running of the conference: registration, issuing
certificates and receipts, etc.